Grade 6: Ratios & Proportional Relationships

This site has content about the Fall 2019 DMA-PD experience focusing on students' understanding of Ratios and Proportional reasoning and how we (teachers) can use assessment to inform instruction.

Students are able to fluently and flexibly make use of

• scalar relationships
• functional relationships

Students understand a ratio as

• a multiplicative comparison of two quantities
• a joining of two quantities in a composed unit (e.g., unit rate)

Student solution strategies can be generally categorized as follows:

• Doubling/Halving

Multiplying or dividing both parts of the original ratio by two repeatedly

• Scalar Additive

Iterating the original ratio by adding it to itself repeatedly

• Scalar Multiplicative

Multiplying both parts of the ratio by a number

• Unit Rate

Reducing the ratio so that one of the parts is 1

• Multiplicative Comparison

Finding missing values of the ratio by looking at how many times one part is compared to the other

Unit Rate and Multiplicative Comparison are the two strategies that can demonstrate functional reasoning. However, the identification of the unit rate could result from either scalar or functional relationships. The image to the left illustrates the differences between these two strategies.